我怎样才能加快这个数组乘法？

Question

for i = 1:N
    for j = 1:M
        for c = 1:3
            A(:,:,c,i) = A(:,:,c,i).*B(:,:,j);
        end
    end
end

是否可以通过矢量化等方式消除最内层循环？

Answer 1

首先你可以通过预乘矩阵来消除j上的循环：

B2 = prod(B, 3); % Element-wise product along third dim

for i = 1:N
    for c = 1:3
        A(:,:,c,i) = A(:,:,c,i) .* B2;
    end
end

然后你可以用repmat把Matrix B2平铺出来，消除另外两个循环。我很难理解 4D 矩阵，但它应该看起来像这样：

B2 = prod(B, 3); % Element-wise product along third dim
B3 = repmat(B2, [1 1 3 N]);
A = A .* B3;

或者（甚至更好）使用 bsxfun：

B2 = prod(B, 3); % Element-wise product along third dim
A = bsxfun(@times, A, B2);

bsxfun 将使用更少的内存，因为它 "virtually replicates" B2.

How can I speed up this array multiplication?